GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Sep 2019, 00:44 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # What is the remainder when X is divided by 40?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager  S
Joined: 18 Feb 2017
Posts: 93
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
IMO A.

Statement 1: 3X + 30 leaves remainder 93 when divided by 120.
The numbers in this form would be 93,213,333,453...
X values for these would respectively would be - 30,70,110,150...
When these values are divided by 40, it always leaves a remainder as 30.
Hence, this statement is sufficient.

Statement 2: 5X - 10 leaves remainder 15 when divided by 20.
The numbers in this form would be 15,35,55,75...
X values for these would respectively would be - 5,9,13,17...
When these values are divided by 40, does not give a fixed value.
Hence, this statement is not sufficient.
Manager  G
Joined: 30 Nov 2017
Posts: 192
WE: Consulting (Consulting)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
The question states that what is the remainder when X is divided by 40

Statement 1: 3X + 30 leaves remainder of 93 when divided by 120

Let X = 21, therefore, 3(21) + 30 = 93
Thus, 93/120 gives remainder of 93
therefore, 93/40 gives remainder of 13

Let X = 61, therefore, 3(61) + 30 = 213
thus, 213/120 gives remainder of 93
therefore, 213/40 gives remainder of 13

similarly, let X = 101, therefore, 3(101) + 30 = 333
thus, 333/120 gives remainder of 93
therefore, 333/40 gives remainder of 13

Therefore this statement is sufficient (AD)

Statement 2: (5X - 10)/20 gives remainder of 15
let X = 5, therefore (5x5 - 10)/20 = 15/20 gives remainder of 15
therefore, 5/40 gives remainder of 5

let X = 9, therefore (5x9 - 10)/20 = 35/20 gives remainder of 15
therefore, 9/40 gives remainder of 9

Not sufficient

Hence answer choice A.
_________________
Be Braver, you cannot cross a chasm in two small jumps...
Director  V
Status: Manager
Joined: 27 Oct 2018
Posts: 630
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
from statement (1),
$$3x + 30 = 120a + 93$$
$$x = 40a + 21$$ , so the possible values of $$x$$ are ($$21,61,101,...$$),
which all gives $$21$$ as a reminder upon dividing by $$40$$ --> sufficient

from statement (2),
$$5x - 10 = 20b + 15$$
$$x = 4b + 5$$, so the possible values of x are ($$5,9,13,...$$)
which gives different values ($$5,9,13,...$$) upon dividing by $$40$$ --> insufficient

A
_________________
Thanks for Kudos
Intern  B
Joined: 16 Jun 2018
Posts: 8
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
IMO A

Have to find: Remainder of $$X/40$$

Statement 1 -> $$\frac{(3X + 30)}{120}$$ gives a remainder of 93. Substitute for X based on this statement. For X = 21, $$\frac{(3X + 30)}{120}$$ gives the remainder of 93 and $$X/40$$ gives a remainder of 21. For X = 101, $$\frac{(3X + 30)}{120}$$ gives the remainder of 93 and $$X/40$$ gives a remainder of 21 again. ---> Sufficient

Statement 2 -> $$\frac{(5X - 10)}{20}$$ gives a remainder of 15. Substitute for X based on this statement. For X = 5, $$\frac{(5X - 10)}{20}$$ gives the remainder 15 and $$X/40$$ gives the remainder 5. For X = 9, $$\frac{(5X - 10)}{20}$$ gives the remainder 15, but $$X/40$$ gives the remainder 9. ---> Insufficient
Manager  S
Joined: 06 Aug 2018
Posts: 98
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
3x +30 will always yield x as 39,79,119 and Soo on

So.remainder will be always 39

But 5x-10 will have values of x different as 13,17 so we have different remainder values

A it is

Posted from my mobile device
Senior Manager  P
Joined: 16 Jan 2019
Posts: 450
Location: India
Concentration: General Management
WE: Sales (Other)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
(1) 3X + 30 leaves remainder 93 when divided by 120.

We can express this fraction as

$$\frac{3(x+10)}{120} = n + \frac{93}{120}$$ where n is the quotient

This reduces to

$$\frac{(x+10)}{40} = n + \frac{31}{40}$$

So when $$x+10$$ is divided by $$40$$, the remainder is $$31$$

When $$10$$ is divided by $$40$$, the remainder is $$10$$ so when $$x$$ is divided by $$40$$, the remainder must be $$21$$

1 is sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.

Lets express this fraction as $$\frac{5(x-2)}{20} = \frac{m+15}{20}$$

This reduces to $$\frac{(x-2)}{4} = m+\frac{3}{4}$$

x-2 leaves a remainder of 3 when divided by 4

Not sufficient to find out the remainder when x is divided by 40

2 is insufficient

Senior Manager  P
Joined: 31 May 2018
Posts: 316
Location: United States
Concentration: Finance, Marketing
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
What is the remainder when positive integer X is divided by 40?

STATEMENT (1) 3X + 30 leaves remainder 93 when divided by 120
from this statement, 3X+30 can be written as
3X+30 = 120K + 93-----(K=0,1,2,3,4........)
3(X+10) = 3(40K+31)
X+10 = 40K+31
X=40K+21

X can be 21,61,101,141.........
X divided by 40 gives the remainder 21
so SUFFICIENT

STATEMENT (2) 5X - 10 leaves remainder 15 when divided by 20.
from this statement, 5X-10 can be written as
5X-10 = 20K+15----(K=0,1,2,3,4......)
5(X-2) = 5(4K+3)
X-2 = 4K+3
X = 4K+5

X can be 5,9,13............45,49,53.....
X divided by 40 gives remainder 5,9,13,...
so INSUFFICIENT

A is the answer
Senior Manager  G
Joined: 13 Feb 2018
Posts: 448
GMAT 1: 640 Q48 V28 Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
We can express x=40q+r
Where q is a quotient and r is the remainder (both non-negative integers)
Always note that remainder cant be more than the divisor (in our case 40)

1 stm --> We can insert above value of x to get:
3(40q+r)+30=120q+3r+30
We can observe that 120q is divisible by 120, so 3r+30 divided by 120 will leave 93 as a remainder
We can manipulate with some noble numbers to get 93 remainder when divided by 120 and those lowest integers are 93 and 213
1) 3x+30=93 r=21 Valid as r<40
2) 3r+ 30=213 r=61 Not Valid r>40
and all other integers will give the value of r more than 40.
Only one option is valid r=21

Sufficient

2 stm --> The same process as above
5(40q+r)-10=200q+5r-10 (200q is divisible by 20)
5r-10 divided by 20 leaves remainder 15
1) 5r-10=15 r=5 (r<40)
2) 5r-10=35 r=9 (r<40)

at least two values are possible

Not sufficient

IMO
ANS: A
Manager  S
Joined: 11 Feb 2018
Posts: 80
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
We are required to find remainder when $$x$$ an unknown positive integer is divided by 40, i.e. the value of "r" where $$x=40m+r$$:

(1) 3X + 30 leaves remainder 93 when divided by 120. - This means that $$3x+30=120n+93$$ ==>> (divide equation by 3) $$x+10=40n+31$$ ==>> $$x=40n+21$$. So the remainder of $$\frac{x}{40}$$ is 21. Sufficient.

(2) 5X - 10 leaves remainder 15 when divided by 20. - This implies that $$5x-10=20k+15$$ ==>> (divide equation by 5) $$x-2=4k+3$$==>>$$x=4k+5$$ ==> $$x=4p+1$$, meaning that when x is divided by 4, the quotient is an integer p and the remainder is 1. However, we are unable to derive the remainder when $$x$$ is divided by 40, insufficient.

Correct answer is A.
Manager  S
Joined: 18 Sep 2018
Posts: 100
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
IMO A

What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.

Say q is quotient, then from st.1 => 3X + 30 = 120q + 93 => 3X = 120q + 63 => X = 40q + 21
Clearly, remainder is 21 when X is divided by 40
Sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.

Say q is quotient, then from st.2 => 5X - 10 = 20q + 15 => 5X = 20q + 25 => X = 4q + 5
Now from this equation we can get X = 5, 9, 13, 17, 21, etc.
And if 5 is divided by 40, the remainder is 5, but if 9 is divided by 40, the remainder is 9
So, we have different values.
Insufficient
Intern  B
Joined: 23 Jul 2017
Posts: 20
Location: India
Concentration: Technology, Entrepreneurship
GPA: 2.16
WE: Other (Other)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
(1) 3X + 30 leaves remainder 93 when divided by 120.
X will be 21, 61 and so on, remainder will always be 21. Sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.
Different remainders for the values of X. Not Sufficient.
Manager  G
Joined: 28 Feb 2014
Posts: 148
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
(1) 3X + 30 leaves remainder 93 when divided by 120.
That means 3x+30-93 is divisible by 120
3x-63 = 120a (where 'a' is a positive integer)
3(x-21)=120a
x-21 = 40a
so we can determine the remainder as 21 when divided by 40. Sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.
5x-25 is divisible by 20
5(x-5)=20a
x-5=4a
We will not be able to calculate remainder when x is divisible by 40 from this equation. Insufficient.

IMO A
Manager  S
Joined: 26 Mar 2019
Posts: 100
Concentration: Finance, Strategy
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
Quote:
What is the remainder when positive integer X is divided by 40?

X is integer and x > 0
We need to identify if it is possible to find a remainder when X is divided by 40 in this Data Sufficiency (DS) question:
Let us analyze the statements:

Statement 1:
(1) 3X + 30 leaves remainder 93 when divided by 120.

Let us write it down as a formula: $$3X + 30 = 120*a + 93$$, where a is the number of times 120 is repeated in 3X + 30
$$3X = 120*a + 93 - 30 = 120*a + 63 = 3 * (40*a + 21)$$
$$X = 40*a + 21$$
Thus, 21 is remainder when X is divided by 40.

Sufficient.

Statement 2:
(2) 5X - 10 leaves remainder 15 when divided by 20.

Again, let us represent it with the formula: $$5X - 10 = 20*b + 15$$, where b is the number of times 20 is repeated in 5X - 10
$$5X = 20*b + 15 + 10 = 20*b + 25 = 5 * (4*b + 5)$$
$$X = 4*b + 5$$
Unfortunately, we do not possess information whether b is equal to 1, 10 or 15, and for this reason are unable to answer the question about the remainder using this statement alone.

Insufficient.

Senior Manager  P
Joined: 12 Dec 2015
Posts: 427
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120. --> correct: 3X+30 = 120*d + 93 => X+10 = 40*d + 31 => X = 40 *d + 21, so if X is divided by 40, the reminder will be 21
(2) 5X - 10 leaves remainder 15 when divided by 20. --> 5X -10 = 20 * D + 15 => X -2 = 4 * D + 3 => X = 4 * D + 5 => X = 4* (D+1) + 1, now case-1: if X =61, then if 61 divided by 4, reminder will be 1 & if 61 divided by 40, reminder will be 21 but case-2: if X =41, then if 41 divided by 4, reminder will be 1 & if 41 divided by 40, reminder will be 1. So different reminder for different cases.

SO the Answer is A
Manager  G
Joined: 18 Jun 2013
Posts: 136
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35 GPA: 3.2
WE: Information Technology (Consulting)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
To find,

Remainder of X when X is divided by 40.

We know,

Dividend = Divisor * Quotient + Remainder

Let us check the two options -

Option 1: 3X + 30 leaves remainder 93 when divided by 120.

=> 3*X + 30 = 120 * Quotient + 93
=> X + 10 = 40 * Quotient + 31
=> X = 40 * Quotient + 21

Hence, X whenever divided by 40 will give a remainder of 21.

Hence option 1 is sufficient.

Option 2: 5X - 10 leaves remainder 15 when divided by 20.

=> 5*X - 10 = 20 * Quotient + 15
=> X - 2 = 4 * Quotient + 3
=> X = 4 * Quotient + 5
=> X = 4 * Quotient + 4 + 1
=> X = 4 * (Quotient + 1) + 1

Hence, X whenever divided by 4 will give a remainder of 1.

Now, if X is 5 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40.
Now, if X is 9 (satisfying above condition in option 2) then it will give a remainder of 9 when divided by 40.
Now, if X is 45 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40.
Now, if X is 53 (satisfying above condition in option 2) then it will give a remainder of 13 when divided by 40.

Hence, option 2 is insufficient.

Manager  G
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
IMO-A

Remainder when positive integer X is divided by 40

(1) 3X + 30 leaves remainder 93 when divided by 120.

3X+30= 120K + 93
=> X+10= 40K + 31 [K = integer]
=> X-21 = 40K
=> X-21= { 0, 40, 80, ........40K}
=> X= 21, 61, 81,....40K+21
Remainder (X/40)= 21

Sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.
=>.5X-10=20K+15
=> 5X= 20K+25
=> X= 4K+5
=> X= {5,9,13,17...........4K+5}
Remainder (X/40)= {5,9,13,17.....}

Not Sufficient
Manager  S
Joined: 17 Jan 2017
Posts: 86
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.

Stmt 1: if x =61, then 3*61+30 = 213 , which results in 93 when divided by 120
if x =141, then 3*141+30 = 453 , which results in 93 when divided by 120.
Different values of X give similar remainder. so sufficient.

Stmt 2: if x =9, then 5*9-10 = 35 , which results in 15 when divided by 20
if x =13, then 5*13-10 = 55 , which results in 15 when divided by 20,
Different values of X give different remainder. so insufficient.

So, the correct answer choice is (A)
Manager  B
Joined: 24 Jun 2019
Posts: 108
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
What is the remainder when positive integer X is divided by 40?

40q+r = X ..... q is quotient and r is remainder. We have to find r.

(1) 3X + 30 leaves remainder 93 when divided by 120.

120q+93 = 3X + 30
120q+63 = 3X
40q+21 = X ... This is in the same form as 40q+r=X

Therefore r = 21

(1) IS SUFFICIENT

(2) 5X - 10 leaves remainder 15 when divided by 20.

20q+15 = 5X-10

20q + 25 = 5X

4q + 5 = X

It is not possible to represent X in the form of 40q+r....

X could be 9 with remainder 9, or x could be 45 with remainder 5.

(2) IS NOT SUFFICIENT

ANSWER: A - 1 Alone is SUFFICIENT
Manager  G
Joined: 15 Jun 2019
Posts: 170
What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.

condition 1,

3x + 30 leaves remainder 93, when divided by 120

assume first no 93, so 3x is 63 hence x is 21. so remainder is 21 if divided by 40

next x will be increased by 120/ coefficient of x ie 120/3 is 40. because other no is just an addition which will always maintain the same distance
so next x is 61 which gives , 183 + 30 is 213, if divided by 120 will leave remainder 93 and so on..
so x can be 21,61,101.... so on . so whatever the remainder is 21 when divided by 40
so this is sufficient, ans is always 21.

condition 2,

5x-10 , remainder 15. when divided by 20

assume n = 15, which gives, 5x = 25 so x =5. , so remainder if divided by 40 is 5

next x will be increased by 20/ coefficient of x ie 20/5 which is 4.
so next x is 5 + 4 is 9, which gives, 45-10, 35 if divided by 20 will leave 15 and so on

x can be 5,9,13,17 .... so on and each leaves different remainder when divided by 40 so clearly insufficient

so ans is A
_________________
please do correct my mistakes that itself a big kudo for me,

thanks

Originally posted by ccheryn on 17 Jul 2019, 12:50.
Last edited by ccheryn on 18 Jul 2019, 04:43, edited 3 times in total.
Manager  S
Joined: 10 Aug 2016
Posts: 68
Location: India
Re: What is the remainder when X is divided by 40?  [#permalink]

### Show Tags

1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
Statement 1 can be written as 3X+30 = 120k+93
Dividing by 3 we get X+10=12k+31 --> X=40k+21.
Dividing by 40 we get X/40 = k+21/40. Remainder is 21.
Hence Statement 1 is sufficient.

(2) 5X - 10 leaves remainder 15 when divided by 20.
Statement 2 can be written as 5X-10=20k+15 --> 5X=20k+25
Dividing by 5 we get X=4k+5
Dividing by 40 we get X/40 = (4k+5)/40
If k = 0, we get remainder as 5.
If k = 1, we get remainder as 9.
Therefore we don't get fixed remainder in this case.
Hence statement 2 is not sufficient.

Statement 1 alone is sufficient. Re: What is the remainder when X is divided by 40?   [#permalink] 17 Jul 2019, 12:51

Go to page   Previous    1   2   3   4    Next  [ 80 posts ]

Display posts from previous: Sort by

# What is the remainder when X is divided by 40?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  